Although
the item response theory, the IRT, has been widely used to test
systems such as the Test of English as a Foreign Language (TOEFL),
it is not yet known to teachers in universities and colleges. The
superiority of the IRT over the classical test method is also valid
in many subjects in universities and high schools. In mathematics
tests, the number of problems to be tested in a short time period
is strictly limited, particularly in universities, which strongly
requires an accurate and efficient method to evaluate the abilities
of students. In this paper, we propose to use the stressstrength
model (the SS), or its Bayes extension (the SSB), to estimate the
studentfs abilities when the abilities are assumed to be the random
variables. In the SS and SSB models, parameters to each problem
are also assumed the random variables. In estimation, we use the
marginal maximum likelihood estimation method and the EM algorithm;
to the SSB, the Bayes estimation method is used in addition. Comparing
the results by the SS and the SSB models with those by the conventional
IRT model, the
SS and the SSB show rather stable estimates. 




evaluation;
item response theory; stress strength model; marginal maximum
likelihood estimation; Bayes estimation; EM algorithm.


